/ x \
x*|- ------ + acot(x)|
| 2 |
1 1 \ 1 + x / x*acot(x)
- - - ---------- + ---------------------- + ---------
2 / 2\ 2 2
2*\1 + x /
$$\frac{x \left(- \frac{x}{x^{2} + 1} + \operatorname{acot}{\left(x \right)}\right)}{2} + \frac{x \operatorname{acot}{\left(x \right)}}{2} - \frac{1}{2} - \frac{1}{2 \left(x^{2} + 1\right)}$$
/ 2 \
| x |
x*|-1 + ------|
| 2|
x x \ 1 + x /
--------- - ------ + --------------- + acot(x)
2 2 2
/ 2\ 1 + x 1 + x
\1 + x /
$$\frac{x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{x}{x^{2} + 1} + \frac{x}{\left(x^{2} + 1\right)^{2}} + \operatorname{acot}{\left(x \right)}$$
/ / 2 \\
| 2 | x ||
| 4*x *|-1 + ------||
| 2 2 | 2||
| 1 3*x 4*x \ 1 + x /|
-|3 - ------ - ------ + --------- + ------------------|
| 2 2 2 2 |
| 1 + x 1 + x / 2\ 1 + x |
\ \1 + x / /
--------------------------------------------------------
2
1 + x
$$- \frac{\frac{4 x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{3 x^{2}}{x^{2} + 1} + \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 3 - \frac{1}{x^{2} + 1}}{x^{2} + 1}$$